Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components

Liverts, Evgeny Z.

doi:10.1103/physreva.94.022506

Cited by 5 publications

(11 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most (but not all!) of the AFCcomponents for k ≤ 4 have been derived in the explicit (analytic) form [23] (see also [25,26] for k ≥ 4). Substantial success in solving the problem can be achieved by the Green's function (GF) approach.…”

Section: The Fock Expansionmentioning

confidence: 99%

“…Using the AFC-components derived in Refs. [23,[25][26][27] we have calculated the coefficients c 1 , c 2L , c 3L and c 2 (of the Fock expansion ( 19)) in the explicit form as functions of the angle θ (see the Appendix). The most of the AFC-components associated with calculation of the coefficient c 3 can be obtained by the method described in Ref.…”

Section: The Fock Expansionmentioning

confidence: 99%

“…where G is the Catalan's constant, has been calculated in Ref. [26]. It characterizes the admixture of the unnormalized HH, Y 21 (α, θ) = sin α cos θ in the AFC-component φ…”

Section: Appendix Amentioning

confidence: 99%

See 2 more Smart Citations

Averaged electron densities of the helium-like atomic systems

Liverts

Krivec

2020

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method [2], the ground state wave functions Ψ of the heliumlike atoms with nucleus charge 1 ≤ Z ≤ 5 are calculated in a few coordinate systems including the hyperspherical coordinates {R, α, θ}. The wave functions Ψ av (R) of the hyperspherical radius R are calculated numerically by averaging Ψ over the hyperspherical angles α and θ. The exact analytic representations for the relative derivatives Ψ av (0)/Ψ av (0) and Ψ av (0)/Ψ av (0) are derived. Analytic approximations very close to the actual Ψ av (R) are obtained. Using actual wave functions Ψ, the one-electron densities ρ(r) are calculated as functions of the electron-nucleus distance r. The relevant derivatives ρ (0)/ρ(0) and ρ (0)/ρ(0) characterizing the behavior of ρ(r) near the nucleus are calculated numerically. Very accurate analytical approximations, representing the actual one-electron density both near the nucleus and far away from it, are derived. All the analytical and numerical results are supplemented with tables and graphs.

show abstract

Section: The Fock Expansionmentioning

confidence: 99%

Section: The Fock Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Averaged electron densities of the helium-like atomic systems

Liverts

Krivec

2020

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Using the original hyperspherical angles α and θ, methods of calculation of the AFCs have been supplemented and extended in the works [15][16][17]. It was proposed [15] to separate the AFCs into the components in the following manner…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in the works [15][16][17] that any component of the AFC can be represented by a single series of the form…”

Section: Introductionmentioning

confidence: 99%

The Green’s function approach to the Fock expansion calculations of two-electron atoms

Liverts¹,

Barnea²

2018

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The renewed Green's function approach to calculating the angular Fock coefficients, ψ k,p (α, θ)is presented. The final formulas are simplified and specified to be applicable for analytical as well as numerical calculations. The Green's function formulas with the hyperspherical angles θ = 0, π (arbitrary α) or α = 0, π (arbitrary θ) are indicated as corresponding to the angular Fock coefficients possessing physical meaning. The most interesting case of θ = 0 corresponding to a collinear arrangement of the particles is studied in detail. It is emphasized that this case represents the generalization of the specific cases of the electron-nucleus (α = 0) and electronelectron (α = π/2) coalescences. It is shown that the Green's function method for θ = 0 enables us to calculate any component/subcomponent of the angular Fock coefficient in the form of a single series representation with arbitrary angle θ. Those cases, where the Green's function approach can not be applied, are thoroughly studied, and the corresponding solutions are found.

show abstract